Our Mathematical Universe

Max Tegmark has a new book out, entitled Our Mathematical Universe, which is getting a lot of attention. I’ve written a review of the book for the Wall Street Journal, which is now available (although now behind a paywall, if not a subscriber, you can try here). There’s also an old blog posting here about the same ideas.

Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an uttery empty vision of the “ultimate nature of reality.” What’s perhaps most remarkable about the book is the respectful reception it seems to be getting, see reviews here, here, here and here. The Financial Times review credits Tegmark as the “academic celebrity” behind the turn of physics to the multiverse:

As recently as the 1990s, most scientists regarded the idea of multiple universes as wild speculation too far out on the fringe to be worth serious discussion. Indeed, in 1998, Max Tegmark, then an up-and-coming young cosmologist at Princeton, received an email from a senior colleague warning him off multiverse research: “Your crackpot papers are not helping you,” it said.

Needless to say, Tegmark persisted in exploring the multiverse as a window on “the ultimate nature of reality”, while making sure also to work on subjects in mainstream cosmology as camouflage for his real enthusiasm. Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone. Now a physics professor at Massachusetts Institute of Technology, he presents his multiverse work to the public in Our Mathematical Universe.

The New Scientist is the comparative voice of reason, with the review there noting that “there does seem to be something a little questionable with this vast multiplication of multiverses”.

The book explains Tegmark’s categorization of multiverse scenarios in terms of “Level”, with Level I just lots of unobservable extensions of what we see, with the same physics, an uncontroversial notion. Level III is the “many-worlds” interpretation of quantum mechanics, which again sticks to our known laws of physics. Level II is where conventional notions of science get left behind, with different physics in other unobservable parts of the universe. This is what has become quite popular the past dozen years, as an excuse for the failure of string theory unification, and it’s what I rant about all too often here.

Tegmark’s innovation is to postulate a new, even more extravagant, “Level IV” multiverse. With the string landscape, you explain any observed physical law as a random solution of the equations of M-theory (whatever they might be…). Tegmark’s idea is to take the same non-explanation explanation, and apply it to explain the equations of M-theory. According to him, all mathematical structures exist, and the equations of M-theory or whatever else governs Level II are just some random mathematical structure, complicated enough to provide something for us to live in. Yes, this really is as spectacularly empty an idea as it seems. Tegmark likes to claim that it has the virtue of no free parameters.

In any multiverse-promoting book, one should look for the part where the author explains what their scenario implies about physics. At Level II, Susskind’s book The Cosmic Landscape could come up with only one bit of information in terms of predictions (the sign of the spatial curvature), and Steve Hsu soon argued that even that one bit isn’t there.

There’s only small part of Tegmark’s book that deals with the testability issue, the end of Chapter 12. His summary of Chapter 12 claims that he has shown:

The Mathematical Universe Hypothesis is in principle testable and falsifiable.

His claim about falsifiability seems to be based on last page of the chapter, about “The Mathematical Regularity Prediction” which is that:

physics research will uncover further mathematical regularities in nature.

This is a prediction not of the Level IV multiverse, but a “prediction” of the idea that our physical laws are based on mathematics. I suppose it’s conceivable that the LHC will discover that at scales above 1 TeV, the only way to understand what we find is not through laws described by mathematics, but, say, by the emotional states of the experimenters. In any case, this isn’t a prediction of Level IV.

On page 354 there is a paragraph explaining not a Level IV prediction, but the possibility of a Level IV prediction. The idea seems to be that if your Level II theory turns out to have the right properties, you might be able to claim that what you see is not just fine-tuned in the parameters of the Level II theory, but also fine-tuned in the space of all mathematical structures. I think an accurate way of characterizing this is that Tegmark is assuming something that has no reason to be true, then invoking something nonsensical (a measure on the space of all mathematical structures). He ends the argument and the paragraph though with:

In other words, while we currently lack direct observational support for the Level IV multiverse, it’s possible that we may get some in the future.

This is pretty much absurd, but in any case, note the standard linguistic trick here: what we’re missing is only “direct” observational support, implying that there’s plenty of “indirect” observational support for the Level IV multiverse.

The interesting question is why anyone would possibly take this seriously. Tegmark first came up with this in 1997, putting on the arXiv this preprint. In this interview, Tegmark explains how three journals rejected the paper, but with John Wheeler’s intervention he managed to get it published in a fourth (Annals of Physics, just before the period it published the (in)famous Bogdanov paper). He also explains that he was careful to do this just after he got a new postdoc (at the IAS), figuring that by the time he had to apply for another job, it would not be in prominent position on his CV.

One answer to the question is Tegmark’s talent as an impresario of physics and devotion to making a splash. Before publishing his first paper, he changed his name from Shapiro to Tegmark (his mother’s name), figuring that there were too many Shapiros in physics for him to get attention with that name, whereas “Tegmark” was much more unusual. In his book he describes his method for posting preprints on the arXiv, before he has finished writing them, with the timing set to get pole position on the day’s listing. Unfortunately there’s very little in the book about his biggest success in this area, getting the Templeton Foundation to give him and Anthony Aguirre nearly $9 million for a “Foundational Questions Institute” (FQXi). Having cash to distribute on this scale has something to do with why Tegmark’s multiverse ideas have gotten so much attention, and why some physicists are respectfully reviewing the book.

A very odd aspect of this whole story is that while Tegmark’s big claim is that Math=Physics, he seems to have little actual interest in mathematics and what it really is as an intellectual subject. There are no mathematicians among those thanked in the acknowledgements, and while “mathematical structures” are invoked in the book as the basis of everything, there’s little to no discussion of the mathematical structures that modern mathematicians find interesting (although the idea of “symmetries” gets a mention). A figure on page 320 gives a graph of mathematical structures which a commenter on mathoverflow calls “truly bizarre” (see here). Perhaps the explanation of all this is somehow Freudian, since Tegmark’s father is the mathematician Harold Shapiro.

The book ends with a plea for scientists to get organized to fight things like

fringe religious groups concerned that questioning their pseudo-scientific claims would erode their power.

and his proposal is that

To teach people what a scientific concept is and how a scientific lifestyle will improve their lives, we need to go about it scientifically: we need new science-advocacy organizations that use all the same scientific marketing and fund-raising tools as the anti-scientific coalition employ. We’ll need to use many of the tools that make scientists cringe, from ads and lobbying to focus groups that identify the most effective sound bites.

There’s an obvious problem here, since Tegmark’s idea of “what a scientific concept is” appears to be rather different than the one I think most scientists have, but he’s going to be the one leading the media campaign. As for the “scientific lifestyle”, this may be unfair, but while I was reading this section of the book my twitter feed was full of pictures from an FQXi-sponsored conference discussing Boltzmann brains and the like on a private resort beach on an island off Puerto Rico. Is that the “scientific lifestyle” Tegmark is referring to? Who really is the fringe group making pseudo-scientific claims here?

Multiverse mania goes way back, with Barrow and Tipler writing The Anthropic Cosmological Principle nearly 30 years ago. The string theory landscape has led to an explosion of promotional multiverse books over the past decade, for instance

Parallel Worlds, Kaku 2004

The cosmic landscape, Susskind, 2005

Many worlds in one, Vilenkin, 2006

The Goldilocks enigma, Davies, 2006

In search of the Multiverse, Gribbin, 2009

From eternity to here, Carroll, 2010

The grand design, Hawking, 2010

The hidden reality, Greene, 2011

Edge of the universe, Halpern, 2012

Watching these come out, I’ve always wondered: where do they go from here? Tegmark is one sort of answer to that. Later this month, Columbia University Press will publish Worlds Without End: The Many Lives of the Multiverse, which at least is written by someone with the proper training for this (a theologian, Mary-Jane Rubenstein).

I’m still though left without an answer to the question of why the scientific community tolerates if not encourages all this. Why does Nature review this kind of thing favorably? Why does this book come with a blurb from Edward Witten? I’m mystified. One ray of hope is philosopher Massimo Pigliucci, whose blog entry about this is Mathematical Universe? I Ain’t Convinced.

After the Level IV multiverse, it’s hard to see where Tegmark can go next. Maybe the answer is his very new Consciousness as a State of Matter, discussed here. Taking a quick look at it, the math looks quite straightforward, his claims it has something to do with consciousness much less so. Based on my time spent with “Our Mathematical Universe”, I’ll leave this to others to look into…

125 Responses to Our Mathematical Universe

One problem I see with the multiverse (and I understand that also includes your Level I) as just another prediction of a theory is that it can be used to justify virtually anything. Suppose another intelligent race (in this universe…) don’t yet know Mawwell’s theory, hit a intellectually wall and are trying to explain the value of the speed of light, which they can measure precisely. A multiverse “theory” can well be used to “explain” it (they happen to live in the the universe where the speed of light is correct). In this sense I am not sure how much the multiverse is really a “prediction” of inflation or a symptom of its weakness in a certain domain. While scientific valuable, the theory most likely cannot be extrapolated to explain, say, the cosmological constant, at least not in a non-environmental way.

PS: I really don’t want to prolong this already confusing discussion. If Max is willing to answer, it would be interesting to read what he thinks – if not, for the rest, please just ignore my comment.

Max,
Sure, a “Level I” multiverse can be an implication of an inflationary theory that you can test, and if you can get enough evidence for that theory you would have evidence for that sort of multiverse. I’m a bit skeptical that you really can get enough info about the inflaton, but sure, this is science.

About the difference between the review and the blog posting. The blog posting was aimed a very different audience, people who regularly read this blog. The aim of the review was to give an accurate picture of what’s in your book, provide some context, explain the main claim you are making, and also explain why it’s empty. I don’t think anyone reading it will miss my argument that this is a book making grandiose but empty claims.

In the blog entry, there’s a part devoted to discussing in detail your claims about testability, there because it wouldn’t fit in the review. Besides that though, the blog entry is really about a different question than the review: why is an even emptier argument than the string theory landscape getting positive attention from the public and some scientists, part of an effective campaign that has already created a highly disturbing situation in theoretical physics? The background for this I’ve written about here ad nauseam, and that context should make it clear to my readers why I’m choosing to begin with a simple and blunt characterization rather than a more polite and indirect one. I don’t think you can really disagree that claims to have figured out the ultimate nature of reality are “grandiose”, and such claims with nothing solid behind them are the province of the crank (note that I think most every theorist feels the allure of this kind of thing, we all have our own inner crank…).

The non-scientific material is there because it’s in your book, and it’s relevant to the main topic of the blog posting, which is non-scientific: why is something that traditionally would be considered crackpot science now making inroads into conventional science? How is that being done? You’re unusual among talented, successful scientists in also having a great talent for getting public attention. You’ve had significant influence in getting people to take seriously highly dubious material about the multiverse. I’m fascinated by how that has happened, although of course my main concern is how to make it stop…

I’m puzzled by the need to invoke inflation to give an example of a theory where there exist regions of a universe inaccessible to certain observers. That can only muddy the waters by the fact that many theoretical as well as observational aspects of inflation are yet to be fully fledged out. On the other hand, already in special relativity, for any single observer (meaning an event on a worldline, or even the whole half of the worldline leading up to an event), there exist spacelike separated regions. In fact, the same thing happens in any theory with a bounded speed of propagation of disturbances (information, or whatever one might call it). All other phenomena like event horizons, Cauchy horizons, cosmological horizons are extensions of this basic property. So, it seems to me that whatever philosophical difficulties are raised by inflation have already been raised by special relativity.

I would be more inclined to look at what the Standard Model does not explain, namely why there are 3 generations of fermions, rather than indulging in rampant ‘modal realism’ or Platonism on steroids. Perhaps getting an answer to that would point to one mathematical structure ‘all the way down’ – to define, rather than merely describe.

Thanks Peter for these helpful clarifications!
I’ve long viewed you as someone who courageously stands up for a controversial view because you feel that it is correct, even thought you get a lot of flack from the physics community for it. This is something I have very much identified with over the years, since as you know, many of my views on physics have been just as controversial as yours, and as a result, both you and I have been called crackpots.

I hope you don’t find this offensive, but I must confess that I find your recent postings disturbingly unscientific. You’re asking the interesting question
“Why is something that traditionally would be considered crackpot science now making inroads into conventional science?”,
so why aren’t you considering all logically possible answers, including the possibility that they’re making inroads because the supporting arguments are actually correct and new supporting evidence has come to light? After all, many currently accepted theories (e.g. relativity theory) were also considered crackpot science by some contemporary pundits. How can you be so certain that it’s a good idea to “work to stop this” if you’re not willing to even consider this possibility? Instead, you appear to dismiss this possibility from the get-go and focus only on other explanations such as the science community having become dysfunctional, me personally having dubious motives, etc.

I also find your posting style disturbingly unscientific, and can’t help feel that you’re applying a double-standard: you keep writing interesting, respectful and carefully balanced replies to me personally about how the Level I multiverse is a valid scientific discussion topic, etc., while at the same time writing pithy sound-bites to others suggesting that everything multiverse-related is unscientific nonsense. To me, one of the core principles of scientific integrity is to only say things that you’re willing to stand by. For example, when I write an anonymous referee report, I like to pretend that I’m going to sign my name under it.

My main goal in this interesting conversation with you is to identify what our common ground is (a lot, it seems!) and where we disagree. My point of view is that we don’t know whether any parallel universes exist or not, but that it’s interesting to explore the possibilities. In contrast, you appear to feel that this is uninteresting, and I totally respect that viewpoint – so far, so good.
Moving on to scientific claims, I make several implication claims in the book of the form “if physics theory X is correct, then multiverse level Y exists”. You still haven’t told me about any physics claims of mine that you feel are incorrect, so unless you tell me otherwise, I’m going to assume you agree with these too. Please let me know if this is a fair characterization of your current views:

* Level I: you agree that it’s a legitimate scientific topic

* Level II: you reject it because of your misgivings about the string landscape

* Level IV: you find this meaningless, but haven’t identified which of my arguments you consider fallacious.

Unless I’ve misunderstood you (and please correct me if I have!), this means that out of the 13 chapters in my book (http://mathematicaluniverse.org – CONTENTS tab), only four (6, 10-12) contain ideas that you feel are a waste of physicists’ time, and your critique of them boils down to mainly to a lack of interest, not to me making incorrect statements in them.
I’m very much looking forward to hearing what you think!
🙂

First about the questions about my views. Sure Level I multiverse theories can be part of legitimate science. In practice though, they are endlessly being abused by people who invoke evidence for them to argue for the string landscape. As Igor Khavkine points out above, the idea that the universe extends indefinitely to unobservable regions, with the same physics, isn’t anything by itself new or revolutionary. My views on Level II are well-known.

About interpretations of QM in general, my view is that the basic laws of QM reflect a very deep mathematical insight into the way the universe works. At a fundamental level, I think that what we still don’t understand very well is how classical mechanics emerges from this (with things like “quantum Darwinism” relevant ideas). “Many worlds” seems to me one legitimate way to characterize the overall picture one is trying to understand. It doesn’t though seem very helpful in getting at what we don’t understand. About the claims in your book relating Level I and Level III, I’ve made no comment, simply because I don’t understand them, and the whole idea just seems too implausible to take seriously. I am committed to only commenting about that which I understand well enough to trust my arguments. An important aspect which I value of the culture of mathematics is an insistence on keeping straight what you understand and what you don’t and always knowing where that boundary is.

On Level IV, yes, I think the arguments you’re making often involve meaningless, ill-defined words and sentences, so one can’t find a “fallacy”. The only way to pin down such arguments is to look for non-trivial implications of them. I tried to be careful in the blog entry to identify the parts of your book that claimed such implications and to explain why I thought they were not justified.

On the other issues you raise, let me make it clear that I don’t think your motives are “dubious”. I’m sure you believe what you are arguing for and people have the right to do what they can to make the most effective arguments for what they believe in. On the other hand, yes I do think parts of the theoretical physics community have become dysfunctional, and my arguments about this are not based on dismissing thoughtlessly the reasons people are doing what they are doing, but upon paying close attention to the issues. By the way, at this point I don’t think the claim that the string theory landscape is dysfunctional science is a controversial minority view of mine, but I’d guess that it’s the majority view in the physics community (maybe even within the “string theory” community, depending how you define that).

As for the claim that I often make crude sound-bite arguments about these issues, I’ll just say that I do the best I can to make accurate statements about what I’m well aware are complicated issues, given the constraints imposed by the format I’m writing in. I was happy with how the WSJ thing came out, partly because I ended up with enough space to make a serious argument and important distinctions. The first draft of that piece was 900 words, which only allowed a serious argument at the cost of so little background that readers got lost. The editor decided to allow a longer (1300 words) piece, which was enough to both give the bare bones of an argument and provide some background. I’m often though in the position of writing something much more constrained by limits of space (or my time), trying to say something in much less than 900 words. This is never going to capture all aspects of the question at hand.

About your book in general, sure, large parts of it are perfectly reasonable discussions of a variety of topics. The problem though is that from the title on, it is structured as an argument for a point of view that I think is seriously misguided, one that is not just a “waste of time”, but is likely to further promote the most problematic trends in this subject. I’ve tried to make clear exactly what my arguments against this point of view are.

As an author of a book myself, I’m well aware that it’s frustrating when people discuss only one aspect of it, ignoring all sorts of things one put into it. It’s true that I’m just ignoring a lot of what’s in the book, just because I have nothing very interesting to say about it. To give one example, when I first saw that you were going to discuss the “singularity”, my knee-jerk reaction was “Oh no, another Kurzweilian technological optimist…”, but when I read that part of the book I saw that I was wrong, you have a much more interesting take on that subject. So, you see, sometimes I can say something positive…

The analogy to relativity is weak. Relativity always had solid experimental support, with Michelson-Morley 1887 and relativistic mass experiments starting in 1902. There is no experimental support for the string landscape, many-worlds, or the math multiverse, nor is there likely to be any in the foreseeable future.

Max, you have labeled your chapters as being “mainstream” or “controversial”. You should not be surprised that the criticism of your book has been centered on the chapters that you labeled controversial.

Since Peter has stated that the Level I multiverse seems methodologically OK and even agreed that it follows from special relativity, do we then have to assent to the argument that there must be a huge number of slightly different copies of ourselves out there, etc.? In other words, is the Borgesian stuff a straightforward logical deduction from the existence of the Level I multiverse or not? And if it is, should we just shrug it off on the basis of its direct unobservability?

srp,
I don’t think we have significant evidence for an infinitely extended universe (or significant evidence against it), just agree that this is a question one can sensibly hope to address by studying various cosmological models and comparing them to experiment. Personally, I’ve never been too interested in the paradoxes that come up when you assume infinite extension, but can see why some people are. To each his or her own…

Since I and many of my colleagues have studied and arrived at many positions similar to those of Mr. Woit, then the conclusion is that you consider our views “controversial” and that some in the community would believe us to be “crackpots.” Perhaps even you? You do not help your cause Sir with such a stand. And in truth you cannot support your position from what is being discussed in the community; I know many in the field of HEP, I have many contacts, I am at a large national lab. Also, I know what is being written. I further resent the insult you make to my intelligence by assuming that I am so naive as to swallow your illogical statements. And your weak attempt to equate yourself with Einstein is obvious when you also characterized general relativity as crackpot to some. After all Hilbert also published the field equations and I sincerely doubt that any reputable scientist would consider the both of them crackpots. Some here have said you are a nice guy. I have never met you and I wonder what motivates you. There is more that could be said. For example “why aren’t you considering all logically possible answers?” To the best of my ability I am considering all my own answers and those I see in the literature. Given what supporting evidence there is, I find some answers to be nonsense and I will not waste my career on them. Life is too short and there is good work to be done. Enough already.

“why is something that traditionally would be considered crackpot science now making inroads into conventional science? ”

See “Physics on the Fringe: Smoke Rings, Circlons, and Alternative Theories of Everything” by Margaret Wertheim (Walker, 2011) [http://physicsonthefringe.com/] for an account of a quantum cosmology meeting at Santa Barbara where conventional scientific constraints on theories were thrown to the wind. The discussions were very similar in atmosphere to those at crank science meetings.

There is very little — if anything — new in Tegmark’s noodlings. Greg Egan famously used the ‘dust hypothesis’ in his Permutation City, and in the linked FAQ, Egan points out that his dust is almost identical to Moravec’s Simulation, Consciousness, Existence paper.

The bottom line? ‘Math is everything’ is fun as a science fictional device, but there’s very little ‘there’ there. This will continue to be the case until there’s some way to tell theories of this type are wrong . . . and you can can get an experimentalist to test for what happens in the requisite setup. Sorry, Max, but science is, above all, a very practical sort of enterprise. Metaphysics need not apply.

I’d just like to say that it’s a little annoying to find that I have to rupture my hump making sure my calculations and research are rigorously fit enough to publish while others can actually make an entire career out of this stuff.

How might one begin to investigate such a claim?
Let’s assume this “new” hypothesis is true and ponder a boundary condition for quick insight. One reasonable boundary condition might be at the onset of the “Big bang.” We have T = 0, E >>0, and I suspect, more than a few other initial condition parameters (please feel free to mentally provide). What’s the status of mathematics at this conjecture? If mathematics is non existent at this point in time, but comes into being only after T=0, then it cannot be our hypothetical constructor. Therefore, let’s assume some mathematics exists at or before T=0. How much mathematics? We surely need enough to define all the universe’s initial conditions. This will take more than a little mathematics – certainly more than all that is known today. Restating then, at the beginning of the universe when T=0, a lot of mathematics (maybe all of it) exists. And where does mathematics exist/reside? Don’t tell me, there is no place in the universe just yet, so let’s define an arbitrary place for it. Will you go for the “Great Omnipotent Depository?” (Something sounds a bit familiar with this concept.) With all this mathematics existing before the universe began, and since the “universe is made of math,” I see we can also conclude that a virtual universe also exists at T=0. WTF, from our original hypothesis, we can conclude that the universe virtually existed before the universe began.

Hmm, I’m sensing more salesmanship than science. Thank you, but I’ll likely pass on this book.

Dear Peter: although I’m grateful for you answering more of my questions, I’m surprised that you didn’t answer the main one!
I’m sorry if I didn’t ask it clearly enough – please let me ask it more explicitly. You’re asking the interesting question
“Why is something that traditionally would be considered crackpot science now making inroads into conventional science?”.
There are of course many possible explanations, including
1) The physics community is becoming increasingly dysfunctional,
2) A “crank” and “impresario” named Max Tegmark with a “taste for grandiose nonsense” is corrupting the physics community,
3) Money from the John Templeton Foundation is corrupting the physics community,
4) They’re making inroads because the supporting arguments are correct and new supporting evidence has come to light.

Your posts above explore options 1), 2) and 3), but isn’t the scientific approach to explore all possibilities, including 4)?
When I talk to physicists other than you, on both sides of the multiverse debate, they routinely mention three explanations in category 4:

a) Observations of the cosmic microwave background by the Planck satellite etc. have make some scientists take cosmological inflation more seriously, and inflation in turn generically predicts (according to the work of Vilenkin, Linde and others) a Level I multiverse.

b) Steven Weinberg’s use of the Level II multiverse to predict dark energy with roughly the correct density before it was observed and awarded the Nobel prize has made some scientists take Level II more seriously.

c) Experimental demonstration that the collapse-free Schrödinger equation applies to ever larger quantum systems appears to have made some scientists take the Level III multiverse more seriously.

Is it really completely obvious that these people are all deluded and that none of these three developments have any bearing on your question?
I can’t help feeling disturbed by similarities between your posts and the recent hate-mail I’ve been receiving from a Young-Earth Creationist: you both seem to start by assuming that your conclusion is true (“Earth is 6000 years old”/“Multiverse ideas are nonsense”), and simply avoid mentioning any evidence to the contrary. If I stop posting on your blog, it will be because your approach is too unscientific for my taste.

About the 3 strongest examples of “experimental evidence” for the multiverse you mention.

First “c”. This is kind of ridiculous. I’ve never heard of anyone expecting QM to fail for such larger systems, so the evidence that it doesn’t can’t possibly have surprised anyone or changed their mind about anything. If it did fail, that would be a huge surprise and would change people’s attitudes dramatically. This is also irrelevant to any of my arguments since I don’t have anything in particular against many-worlds interpretations (although I also don’t think they get at the interesting questions). On the other hand, if you have any evidence for your cosmological interpretation of QM that would be different, but I saw none in your book.

About “a”. Again, I’m not arguing against Level I multiverses. On the question of eternal inflation, from what I can tell we still have little to no relevant experimental evidence, although I freely admit to not being an expert on this. Since you are one, here’s a question: later this year Planck will release B-mode polarization results. What does eternal inflation say about this? If Planck sees nothing, will that be evidence against inflation and people will start having less faith in an eternal inflation scenario and thus such a multiverse? If this is a subject with real connection to experiment, what’s the prediction here?

About “b”. Obviously I’m well aware of the Weinberg argument about the CC (it’s basically the only one anyone ever brings up for a Level II multiverse). Sure, I agree that that argument and the observed value of the CC have had an influence. I don’t happen to think it’s particularly strong evidence, but, sure, it’s at least something. No, I don’t argue that anyone interested in Level II multiverse theories is a fool with no reason to be thinking about this.

As for the three explanations you have me making for interest in the Level II multiverse (as opposed to your fourth claimed correct one that it is due to increased support from experiment and better theoretical understanding), first of all, you’re ignoring the main one I am making: people who have a lot invested in string theory refusing to admit their theory has turned out to be an empty failure. Do you honestly claim this is not a major contributor to interest in the Level II multiverse?

Of the three explanations you do assign to me, about Templeton I do think their money has had some effect, I don’t know how much. Maybe increased interest in the multiverse in the last ten years was not affected at all by things they financed, like the 2003 “Universe or Multiverse” Stanford conference and the book that came of it. I suspect they think their money has an effect or they wouldn’t have kept spending it. I don’t think it’s deniable that, at least in 2003, the NSF was not about to finance such a conference. In an alternate part of the multiverse where John Templeton died a pauper, I think it’s fair to suspect there might be slightly less interest in the multiverse.

About your influence, again I’d find it hard to quantify, but it’s non-zero. Recall that no less a source than the Financial Times tells us “Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone.” As for terminology, applying “impresario” to your FQXi activities and others seems to me rather accurate. To be accurate, I referred to you not as a “crank”, but as a scientist who, with this book and the Level IV business in general, was “indulging his inner crank”. Do you honestly have no idea what your colleagues think about this kind of thing? How many do you think believe the Level IV business is anything other than empty grandiose nonsense of a characteristically crank or crackpot sort?

As for the comparison of me to a Young-Earth creationist spewing hate-mail, get a grip.

One comment on Templeton and the multiverse, if I may. As I understand it, maybe I am wrong, Templeton is interested in financing research that links science to god, or as they say in their mission statement, the “spiritual dimension.” The multiverse is used by materialists to explain fine tuning and other existential “mysteries” as an alternative to god. I don’t think Templeton has any great interest in promoting the multiverse.

This has been a very spirited and interesting debate. I would like to propose a compromise which I believe both sides can agree on. The mathematical universe hypothesis is a religious principle.
–
There seem to be two options to explain the existence of our universe in light of the fine tuning required for us to be here: (1) God made it that way, or (2) all mathematically possible structures exist. If there is a third option, then Mr Woit should be able to identify a specific flaw in Mr. Tegmark’s reasoning. So far, I haven’t seen one.
–
Mr. Tegmark’s proposal provides a logical foundation for the religion of atheism. For any physicist with faith in determinism (and how can we have physics without that faith?) Mr. Tegmark’s conclusion is unavoidable. With that said, I personally can’t imagine any scenario where this hypothesis would be falsifiable. Of course, that should not detract from its value for inspiration and clear thinking.
–
Mr. Woit’s criticism is based not on a critique of Mr. Tegmark’s logic, but rather on a religious belief in God, free will, or a more traditional notion of our world. I don’t see how this opposition can be reconciled with the basic assumptions that external reality exists and that physics can describe it, but it too is based on sound religious notions.
–
Of course, if this debate is really about who should get funding for what then these comments don’t really add anything to the debate so feel free to ignore them.

Max – to be fair as much as I don’t like the Lubos Motl type of language e.g. “crank”, I was clear that Peter was referring to particular ideas rather than you as a person. I don’t personally see the harm in putting forward any idea however outlandish as long as we do not give the lay person (or even the reasonably well-informed person) the idea that what we are saying is experimentally confirmed fact.
I have found what you have to say very interesting and as someone elsewhere said, you are at your most impressive when you ignore the stuff other people would take personally (hard to do, easy to admire).

Neil,
Templeton’s agenda is more interesting and subtle than just linking science and religion, and promoting religion (although they do plenty of that). If you look at what they don’t support, they’re explicit about not supporting experiment, and they pretty much avoid serious mathematics. One could say they like to support “philosophy”, and their “philosophy of cosmology” initiative is part of this. I don’t think they have a side pro or con on the multiverse, but it definitely is a topic they like to support discussions of. All in all, they like to support ideas and work that the scientific community doesn’t normally support because it seems rather empty and unlikely to be fruitful. Some of this ends up supporting actually interesting work, some is just a waste of time, and, yes, going on about religion and science fits nicely into this.

One way of describing the effect they’re going for (and to some extent achieving) is to move topics like “universe or multiverse” from the category where the consensus is “empty waste of time, best ignored” to “controversial” (i.e. worthy of debate).

I was going to stay out of this debate, having in print already two books that explain why anthropic multiverse cosmologies cannot possibly yield falsifiable predictions. These books, Life of the Cosmos and Time Reborn, also put forth also an alternative program for cosmology that does yield falsifiable predictions, based on the hypothesis that laws evolve in time.

But I don’t want to let pass Max’s claim that Weinberg’s prediction of the order of magnitude of the dark energy provides evidence for a multiverse. Weinberg’s prediction happened to turn out roughly right but the argument that that provides evidence for the multiverse is based on fallacious reasoning. I explained why on page 136 of Time Reborn, from which I quote:

“One problem with that conclusion is that the critical value referred to is the one above which galaxies would not form if the cosmological constant were the only parameter that varied. But theories of the early universe have other parameters that can vary. If we vary some of those while we vary the cosmological constant, the argument loses its force.

Let’s look at one case, in which we vary the size of the density fluctuations, which, as we discussed earlier in this chapter, determine how evenly the matter in the early universe was distributed. These are relevant because if they were bigger, the cosmological constant could be far above the critical value and galaxies would still form in the very dense regions created by the fluctuations. There is still a critical value for the cosmological constant, but it goes up as the size of the density fluctuations goes up.

So you can rerun the argument, letting the cosmological constant and the fluctuation size both vary over the population of universes. Now you pull two numbers out of the hat for each universe, one for the cosmological constant, the second for the size of the density fluctuations. We choose these numbers randomly, within the range in which galaxies form. It turns out that the probability of randomly getting both numbers to be as small as they are observed to be is now down from 1 chance in 20 to a few parts in 100,000.

The problem is that because we don’t observe any other universes, it is impossible to know which constants vary over the hypothetical multiverse. If we assume that the right story is that only the cosmolog- ical constant can vary over the multiverse, Weinberg’s argument does well. If we assume that the right story is instead that both the cosmological constant and the fluctuation size vary, the argument does less
well. In the absence of any independent evidence as to which, if any, of these hypotheses are true, the argument leads to no conclusion.

So the claim that Weinberg’s argument correctly predicted the rough value of the cosmological constant fails, because of a subtler fallacy than the one discussed above. This fallacy, which is known to specialists in probability theory, arises whenever you take advantage of the freedom to arbitrarily choose a probability distribution that describes unobservable entities and so cannot be checked independently. Weinberg’s original argument has no logical force, because you could reach a different conclusion by making a different assumption about unobservable entities.”

(there are citations to the scientific literature in the text.)

Max, do you have a response to this or do you agree that Weinberg’s argument offers no evidence for a multiverse?

Thanks Lee,
It did occur to me after writing that comment about this that referring to your arguments about this would have been a good idea.

Another thing I could have added was the following simple point I often tried to make in arguments about this way back when. The Level II Multiverse theory of the CC is effectively the same as my own personal theory of the CC, which is that I have absolutely no idea what is responsible for its value. So, hey, no reason to think any particular value is more or less likely. I think the implications of the Level II Multiverse theory and my theory of the CC thus should be the same: from nothing you get nothing.

“But theories of the early universe have other parameters that can vary.”

I was under the impression that in these multiverse theories one was allowed to do anything. In the book “Universe of Multiverse” ()http://books.google.se/books?id=U_Jm2DT_AVAC&printsec=frontcover#v=onepage&q&f=false on part II, when Craig J. Hogan enters with particle physics he is talking about changes in the Yukawa couplings – which by itself, could give you almost anything given enough creativity. I suppose the multiverse should even make SUSY irrelevant since it can also solve the hierarchy problem.

First, I have read both Our Mathematical Universe and Time Reborn and enjoyed them both very much. I view them as popular novels appealing to a wider audience that presents both non-controversial as well as controversial ideas. I see no problem with presenting or even pushing controversial ideas provided there is no attempt to deceive. Neither book was deceptive, so there is no issue. Furthermore, these controversial ideas are often exciting and effective in attracting a wider and uninitiated audience to the subject.

Second, I appreciate the obvious importance in questioning the falsifiability of theories, as long as this process itself is carried out scientifically – lest you become a hypocrite. What I see absolutely no value in is attacking and dismissing admittedly controversial ideas outright simply because you find them exceedingly peculiar or fear their potential effects on the direction of the field, provided of course that they have some merit – which is for the field to decide. Indeed, I can easily imagine negative effects resulting from these kinds of (unscientific) attacks being much more plausible than some critical number of students being misled into studying “empty” theories and this resulting in some crisis of the field – this would require severe misjudgment on a large scale in a manner that is not compatible with the typical student of physics. In short, it’s a needless concern and appears to me to be a cop-out for more legitimate forms of dismissal.

Third, radical theories, both good and bad, must often be “sold” if they are to find wide-spread acceptance – it just follows logically from the nature of revolutionary ideas and is supported by the history of physics.

Finally, being a PhD student in physics I can tell you that it wasn’t very-well founded, falsifiable ideas that got me interested in physics. It was reading Thorne’s “Black holes and time warps” and Kaku’s “Hyperspace” as a child, which then led to Bertrand Russell’s “ABC of Relativity” and more “non-controversial” material.

Finally, finally – REAL crises do exist such as global warming and nuclear proliferation that scientists are going to need to get comfortable speaking about with some emotion and zeal that they are not characteristically known for – hell, it would even be great if we had a few “academic celebrities” – because if we don’t sell these issues to the public then there won’t be any meaningful landscape left to falsify.

The “Mathematical Universe Hypothesis” and Level IV multiverse of Tegmark’s book is not “controversial”. As far as I can tell, no serious scientist other than him thinks these are non-empty ideas. There is a controversy over the string theory landscape, but none here. These ideas are also not “radical”, they are content-free.

You refer to Tegmark’s book as a “novel”, and then you expect it to inspire young people about science, and convince the public to take scientist’s warnings about global warming seriously. This makes no sense. What will inspire smart young people to be scientists is good science, not obviously empty claims. I don’t think this book helps the credibility of scientists with the public one bit, quite the opposite. Yes, scientists sometimes need to sell their work to the public. But to do this, they have to have something of value to sell.

I made a joke to him about our weather vs. East Coast weather during the setting-up period, but had no chance to talk to him during the now-obligatory book-signing period, which appeared to be about 30-50 people long. (I bought the book via Amazon and it arrive on the day of official pub, the 17th).

He said little about multiple universes. I thought his talk was very good at what I’ll call the “George Gamow, One, Two, Three Infinity” level. Understand, this was a book that mightily influenced me in the 60s when I was about 12.

(To my left in the crowd was a woman with a young boy. Tegmark spoke directly to a few of the young kids (boys) in the audience. This boy said he was 9. Tegmark asked him about his interests. “Chemistry” was not terribly surprising. But he also asked about some sums, and the kid responded correctly. And he sat during the presentation paying rapt attention, apparently. (One has to be careful about observing others, the Heisenberg Pedophelia Principle.)

So, Tegmark did a nice prevention about the frontiers of astronomy (the Hubble Deep-Field), some mentions of some stuff possibly beyond, but he did not discuss the controversial aspects of his MUH theory.

(As we were dispersing, I hear one very famous UCSC professor saying “Well, it was good that there were no questions about alternate universes.” I overheard him and quipped “Don’t worry, in 10 to the 700 other universes they asked questions.”)

My feeling is that Tegmark’s lecture, and his book, which I have skimmed since receiving it last week, are not terrible things for people to read.

I grew up on reading Gamow, Asimov, etc. on popular science, plus the then-excellent Scientific American. The weird stuff about monopoles, tachyons, etc. was out there, but one developed a good idea of what was plausible and what was longer-term, somewhat implausible.

As a long-time reader of Peter Woit’s blog, and his book, but as someone who also reads Lubo Motl’s blog, I think Tegmark’s books is a fairly good popularization of some background in physics and cosmology and and an introduction to the more outré aspects.

(Sorry to be personal, but string theory never grabbed me. But the recent EPR = ER stuff really, really grabs be. Doesn’t make it right. But it sure is suggestive.)

Thanks for responding – this comment thread got blown up! Aside from addressing the validity of an idea, which is clearly totally worthwhile and necessary, I was trying to speak to other separate issues which I will try to be a bit more clear about.

1) The concern that MUH will lead the field astray and waste time that could be better spent elsewhere: I was trying to say that I think this is unlikely. A similar argument has been made about string theory and the landscape, yet physics appears to not have imploded yet nor does it appear to be approaching a crisis. I’m not saying that MUH has the legitimacy or establishment that string theory has found, nor am I saying it is without merit. Nor had Max even remotely tried to claim this is an accepted mainstream idea. And this will all be clear to anyone serious about physics. So this entire concern is unwarranted.

2) Young people may be inspired toward science by ideas that stir their curiosity and which they find intellectually fascinating. This can be “good science”, science fiction, or anything in between. But above all it must be interesting. What will make them “good scientists” is the entire formal process required to become a scientist. I have more than a few friends who were originally inspired to pursue science from Star Wars.

3) There is nothing inherently wrong with “grandiose” ideas, being an “academic celebrity” or selling one’s ideas. In fact, these qualities are currently needed more among scientists to appeal to the public about pressing social issues. This was a statement about the virtue of these traits alone, which were mentioned somewhat derogatorily in previous posts, and not with respect to the book or the books role in promoting awareness about global warming. And, unfortunately, it is not the credibility of scientists that pushes part of the population toward climate change denial – it’s the loudness, visibility and grandiosity of (totally incredible) pundits.

The overall point being that both Max and his more fun ideas have a net positive effect on both science and the world we live in.

I can’t help but question why you felt the need to mention about your own work and its ability to make falsifiable predictions. I think this is maybe a little bit rich, considering that charges of empty content and the rest could easily be pointed in your direction with regards to your recent book and arguments and claims concerning the reality of time. That is, time and the empirical don’t, and will never, go together.

My logic, as was carefully explained in Time Reborn (TR), takes three steps, which in outline are:

1) The various arguments which have been given that time is an illusion, i.e. emergent from a more fundamental timeless level of description, depends on an assumption, which is the immutability of the laws of physics. This is one of the conclusions of Part I of TR.

2) Specific hypotheses about how the laws evolved are testible by real,doable experiments and observations, a few are even falsifiable.

3) Therefor, if a hypothesis that laws evolve were confirmed by evidence, the laws cannot be immutable, therefor the arguments that have convinced physicists that time is unreal would have no force.

So there is a relationship between the view of time and empiricaly testible hypotheses.

Furthermore, the hypothesis of cosmological natural selection, published in 1992, made two falsifiable predictions which continue to stand up to empirical test. It also remains the only proposed explanation for the fine tunings of the standard model that makes falsifiable predictions.

IMO that 3 step argument must surely be the most interesting thing that has appeared in this thread and contains what could be the REAL reason that the natural world appears mathematical.
Since Max T. seems to like mathematical regularities/patterns, this argument, I suspect, is what the second half of his MUH book should actually have been about:

Leibniz principle of sufficient reason (for the manifest regularity Wigner referred to) implies TIME = a process by which regularities emerge and become “laws”

Thermodynamics of physical law. The universe becomes more predictable as time goes on. More “mathematical” more patterned, more regulated, more repetitive. Paradoxically beautiful and from another perspective boring: more expected and less surprising.
Like a Shannon channel whose information capacity is gradually diminishing until the listener at the other end hears nothing, or nothing he didn’t already know.

So this three step argument shows us the real MUH. And there is only ONE universe in this MUH. It is unnecessary, old-fashioned, and ridiculous to imagine more than one.

Leibniz+Wigner –>time, and time is “testable” in the sense that we might someday witness the emergence of an unprecedented regular pattern.

Extremely farfetched, but still nice.

The first half of Tegmark’s book, from what I have sampled, is pedagogically excellent. It reminds me of Timothy Ferris’ *Coming of Age in the Milky Way*, really A-plus. Maybe it is such a good front end that it should have a different back end. :0)

Thanks. There is more I’d like to say than this, but I agree that it would be off topic. If I can, though, I would like to quickly mention that, unless one is very selective, arguments for time’s non existence don’t depend on the assumption that the laws of physics are immutable (I can think of plenty that aren’t, including simply that time is unobservable). The thesis that the laws of physics should be mutable and internal to the universe (I don’t think there can be any doubt that the latter is correct) also obviously isn’t dependent on time existing.

While I disagree with his ideas, I think Max deserves credit for participating in this discussion. Hopefully he’ll come back. If he does, I think some sensitivity to his position (maybe a bit like an English soccer supporter walking into a rival team’s local bar) wouldn’t go amiss.

I was also at that Santa Cruz bookstore lecture. I was surprised that he peppered his talk with arguments that we are not spending enough money and effort trying to reduce risk of future disasters. His math multiverse implies that time is an illusion, that we have no free will, and that all future scenarios happen, regardless of what we might try to prevent.

> Max, do you have a response to this or do you agree that Weinberg’s argument offers
> no evidence for a multiverse?
I fully agree with the mathematics in your analysis. In fact, I reached a similar conclusion in http://arxiv.org/pdf/astro-ph/0410281v2.pdf (see around 81), and so does Alex Vilenkin. The bottom line is that galaxy formation efficiency depends not on the dark energy density alone, but on what we might call the dimensionless “Weinberg” parameter W=rhoL/Q^3 xi^4, where Q ~ 2e-5 is the CMB fluctuation level, rhoL ~1e-123 is the dark energy density and xi~2e-28 is the dark matter density per photon, all in Planck units. What Weinberg’s argument gives is then a prediction for the parameter W, no more and no less. Vilenkin has emphatically argued that Weinberg’s prediction for W is impressive because it predated its measurement (by observations of CMB, supernovae, etc).

Max,
There is no “controversy” about your MUH and Level IV arguments, just a consensus that they are empty, and that’s what you need to address.

I notice that you have decided to stop answering any of the arguments I raise, in favor of a sleazy tactic of slandering me as a creationist. Up to you how to behave, I don’t think you’ll find this helps you or your case.

Peter, it’s not fair to ask Max (or anyone) to address a claim that the MUH is “empty” if you don’t define what that means. Do you mean only that you think it is unfalsifiable? Or do you believe that it is “empty” philosophically as well? You keep saying it over and over, but nowhere in this thread or in your original post do you present an argument for anyone to rebut. One might say your criticism is “empty.” Some in this thread have presented examples of how the MUH may turn out to be predictive. You completely ignore these arguments (sometimes removing them from the comment section) and just keep shouting “empty!” without addressing their points. Even your reaction to the recent discussion of the Weinberg argument (“I don’t happen to think it’s particularly strong evidence, but, sure, it’s at least something.”) is perplexing in the context of your statement that the MUH is “completely empty”. Completely? You just admitted that the L2 multiverse has perhaps some weak predictive content! So you really need to be clear about exactly what you mean by “completely empty” before asking others to defend against an attack that is itself “completely empty” in its current form.

Hi John: Peter Woit’s latest accusation that I’m somehow claiming that he’s a creationist is so silly that it hardly warrants a reply. Please let me repeat and expand on what I wrote above, in the hope that it won’t be further misunderstood.

I wrote that I couldn’t help feeling disturbed by similarities in argumentation style between Peter’s posts and the recent hate-mail I’ve been receiving from a Young-Earth Creationist: both seem to start by assuming that their conclusion is true (“Earth is 6000 years old”/“Multiverse ideas are nonsense”), and they then proceed to simply avoid mentioning any evidence to the contrary. I gave a detailed example of how Peter did this in my January 22, 2014 at 6:44 pm post above, by avoiding any examination of option 4. To me, this is an unscientific approach. As far as I can tell, the posters on that creationist site I linked to appear to dislike my book because they feel it represents a naturalistic world view. Again, they don’t appear interested in examining all logically possible options (in particular, the logically possible option that modern cosmology is correct), instead dismissing this with pithy quotes about “nonsense”, “crank” etc. that they’ve borrowed from Peter Woit. If we scientists are to have any claim to the moral high ground in scientific debates, I feel that we need to practice what we preach and conduct our debates at a higher level of civility and rigor!

Max,
While pointing to your January 22 comment, you studiously ignore my response to it, following up your attack on me as similar to a hate-mail-sending Creationist with a sleazy comment about my supposed connection to a “disturbing” ID blog. You then end with “I feel that we need to practice what we preach and conduct our debates at a higher level of civility and rigor!”. Impressive.

By the way, I just noticed that you’re featured in an upcoming film, The Principle. Have you seen it, and if so do you think you do a good job of representing the scientific viewpoint in this film?

I devoted a fair amount of time to carefully reading the Tegmark book and looking for where he discussed the implications for physics. In the blog entry above I discussed those carefully and completely, giving an argument (that no one has contradicted) that Tegmark was unable to derive and real implications of his MUH or Level IV multiverse for physics. This has nothing to do with the argument about Level II predictions.

Peter, then I suggest you add the adverb “currently” before your use of the word “empty.” Even more fair would be “currently not predictive.” There is a big difference between being vacuous (which is what “empty” may imply) , and simply being a theory that may or may not yield testable predictions at this time. The argument you need to be making then, is why you are so sure that this theory has no possibility whatsoever of ever yielding testable predictions. I have not seen this argument from you, and I think it is an argument that needs to be made if you really believe that the MUH is not worthy of further study. I have a hard time believing that you could really hold such a hard line, when it is so obvious (from arguments like Weinberg’s discussed above) that there really can be no possibility of predictive consequences of such a theory (the Level II apropos of Winberg is not level IV, but in theory the logic is no different).

Orin,
The problem is not one of “currently untestable”, but one of “in principle untestable”. Tegmark is the one who wrote scientific papers and a book about this, he’s the one responsible for explaining why the ideas are not vacuous, by giving a plausible explanation for how his ideas could be tested, at least in principle. The burden of proof is not on me, but on him. I’ve argued above carefully above that he hasn’t met this burden (although he claims in his book that he has).

If you follow the discussion between us in these comments, I think you’ll see that the point at which he starts going on about hate-filled creationists is the point where he no longer has an argument. That’s what people do…

Peter, you well know that an idea exists independently of a promoter of that idea. To insist that you will only accept an argument from Max and only Max is a bizarre form of straw man. There have been examples given in this thread of how the MUH is not necessarily vacuous. You have ignored them.

Orin,
You seem to find it plausible that Tegmark wrote a whole book about his “hypothesis”, but didn’t bother to include in the book an explanation of how his “hypothesis” could be tested. Now, before I can argue that he doesn’t have anything, it’s my job to prove that there’s no way for anyone to come up with tests for his “hypothesis”. Right? Sorry, we disagree, I think my job is to read the book, assume he has put his best arguments in there, and see if these arguments are convincing, or if they don’t hold water. I think any scientist who reads the book will see that the latter is what is going on here.

By the way, have you read the book? On which page did you see a convincing argument from him that his “hypothesis” was testable?

Peter, I’m afraid I haven’t had the time to read the book yet, but I’m familiar with the material I expect to be in it. Hopefully I’ll get to it next week. I will admit that if what you say is correct then I am puzzled that Max would not include in his book the interesting ways in which the MUH can lead to physical predictions. Of course I know well from your past opinions that you don’t take kindly to some of the tools that would be brought to bare, such as anthropic reasoning(*). Nonetheless such reasoning is not vacuous, it exists independently of whether or not Max puts it in his book, and you are surely aware of it, so it seems disingenuous to take such a hard line as “vacuous” with regard to these ideas. It would be refreshing if you admitted that in principle these ideas could yield fruit. Could they not?

(*) I should note that this is by no means the only reasoning; it may not even be necessary if a sensible measure is found to be predictive.